The present invention relates to an advanced use of natural gas, biogas and methane hydrate which contain methane as a main component. Natural gas, biogas and methane hydrate are regarded as effective energy resources against global warming, and therefore an interest in techniques using them has grown. A methane resource is expected to be a novel organic resource in the next generation or to be a hydrogen resource for use in fuel cells, by putting a clean characteristic of methane to full use. More particularly, the present invention relates to: a catalyst chemistry conversion technique for efficiently producing aromatic compounds exemplified by benzene and naphthalene which are materials of chemical products such as plastics, and high purity hydrogen, from methane; and a method for producing the catalyst.